Heinz von Foerster Festschrift

The Koans of HvF

Koans have always held a great fascination for me. Koans are those strange questions a Zen teacher asks his disciples.

There is no given answer to these questions in the given logic. Each disciple has to find his own answer. Only the master can accept the answer, an answer that must not consist of spoken words. It can also be the moving of a cup of tea or another strange -form an observer's perspective- action.

The most famous Koan is the question about "The Sound of One Hand": "You can hear the sound of two hands when they clap together. Now show me the sound of one hand?"

For a long time this question didn't make any sense to me and I pushed it away for many years. But while dealing with constructivism and Heinz Von Foerster the "Sound of One Hand" came all of a sudden back to me and confused me.

I asked myself: "What is this all about: A subject hits the object and thus produces a sound? Does sound exist at all? How is the materialworld created?"

I understood that it is not the answer that is important for the Koans. Important is to change one's own perception.

In the same way do HVF's short statements function such as the "undecidable questions", the "trivial and non-trivial machines" and so on. Dealing with these statements does not lead to more knowledge, to answers but to a different perception.

After the "Sound of One Hand" I was occupied with HvF's equation:

Xn+1 = OP (Xn)

Or its special form

X1 = OP (X0)

What is remarkable with this equation is, as Heinz von Foerster states, that it is recursive.

When we perform a certain operation with an initial number (X0) we produce X1. When we go on with the same operation with X1 we produce X2. The basic principle in a recursive process is that we reenter the outcome of the operation into the same operation. This process has the fascinating result that it leads always to the same outcome if we continue long enough.

As an example HVF shows that we get a smaller number if we extract the square root of this number. If we extract the root again we get an even smaller number. If we continue this process the result will be 1. And this result is independent of the initial number. The operator determines the result.

When I read this for the first time I had a new Koan. For months no day went by without my being occupied by this equation. It changed my perception. The world changed, became more transparent, required more responsibility.

An example for such a change is my psychotherapeutical practice. In almost every therapy I torture my clients with HVF's equation. I usually use it when a client says that he or she would need a different partner, a different country or a different situation. By using the equation I explain that it does not make any sense to change the partner, the country or the work as long as the operator, i.e. the way of living, perceiving, structuring or constructing one's own live remains as it was before. Sooner or later the outcome will be the same. With a new partner things seem to look promising in the beginning, or using the square root example again: there is an interesting number. But after some time the result becomes more and more usual with the new partner as well as in extracting the square root. And the end is the same boring 1.

The important thing in psychotherapy (as well as in my own live) is to change the operator not the operand.

When I was first concerned with this subject I came into contact with HVF. (The Buddhists say that the teacher comes when the disciple is ready.) And HVF strongly believes that it is more important how we perceive as it is important what we perceive.

But this simple form of recursive processes is - as the master points out- only true for trivial machines.

But this is probably a different koan.

Georg Ivanovas

Heinz von Foerster Festschrift